Problem: Calculate the quotient below and give your answer in scientific notation. ${\dfrac{2.85\times 10^{6}}{30{,}000}} =\ ?$
First, let's change the number in the denominator into scientific notation. ${\dfrac{2.85\times 10^{6}}{30{,}000}} = {\dfrac{2.85\times 10^{6}}{3.0\times 10^{4}}}$ Start by collecting the significands and exponents. $ {\dfrac {{2.85} \times {10^{6}}} {{3.0} \times {10^{4}}} = {\dfrac{2.85}{3.0}} \times {\dfrac{10^{6}}{10^{4}}}} $ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= {0.95} \times {10^{6 \,-\, 4}}$ $= {0.95} \times {10^{2}}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$. In this case, we need to move the decimal one position to the right without changing the value of our answer. We can use the fact that ${0.95}$ is the same as ${9.5 \div 10}$, or ${9.5 \times 10^{-1}}$. $ = {9.5 \times 10^{-1}} \times {10^{2}} $ $ = 9.5 \times 10^{{-1} + {2}} $ $= 9.5\times 10^{1}$